501
Views
90
CrossRef citations to date
0
Altmetric
Original Articles

Stability Investigations of Multivariable Regression Models Derived from Low- and High-Dimensional Data

, &
Pages 1206-1231 | Received 20 Apr 2011, Accepted 10 Jun 2011, Published online: 24 Oct 2011

REFERENCES

  • Altman , D. G. , Andersen , P. K. ( 1989 ). Bootstrap investigation of the stability of a Cox regression model . Stat. Med. 8 : 771 – 783 .
  • Augustin , N. , Sauerbrei , W. , Schumacher , M. ( 2005 ). The practical utility of incorporating model selection uncertainty into prognostic models for survival data . Stat. Model. 5 : 95 – 118 .
  • Austin , P. C. , Tu , J. V. ( 2004 ). Bootstrap methods for developing predictive models . Am. Stat. 58 : 131 – 137 .
  • Binder , H. , Schumacher , M. ( 2008a ). Adapting prediction error estimates for biased complexity selection in high-dimensional bootstrap samples . Stat. Appl. Genet. Mol. Biol. 7 : article 12 .
  • Binder , H. , Schumacher , M. ( 2008b ). Allowing for mandatory covariates in boosting estimation of sparse high-dimensional survival models . BMC Bioinformatics 9 : 14 .
  • Binder , H. , Sauerbrei , W. ( 2009 ). Stability analysis of an additive spline model for respiratory health data by using knot removal . J. R. Stat. Soc. Ser. C 58 : 577 – 600 .
  • Bøvelstad , H. M. , Nygård , S. , Størvold , H. L. , Aldrin , M. , Borgan Frigessi , A. , Lingjærde , O. C. ( 2007 ). Predicting survival from microarray data—A comparative study . Bioinformatics 23 : 2080 – 2087 .
  • Boulesteix , A.-L. , Slawski , M. ( 2009 ). Stability and aggregation of ranked gene lists . Briefings Bioinformatics 10 : 556 – 568 .
  • Boulesteix , A.-L. , Guillemot , V. , Sauerbrei , W. ( 2011 ). Use of pre-transformation to cope with extreme values in important candidate features . Biometr. J. 53 : 673 – 688 .
  • Breiman , L. ( 1992 ). The little bootstrap and other methods for dimensionality selection in regression: X-fixed prediction error . J. Am. Stat. Assoc. 87 : 738 – 754 .
  • Breiman , L. ( 1993 ). Fitting additive models to regression data: Diagnostics and alternative views . Comput. Stat. Data Anal. 15 : 13 – 46 .
  • Breiman , L. ( 1995 ). Better subset regression using the nonnegative garrotte . Technometrics 37 : 373 – 384 .
  • Breiman , L. ( 1996 ). Heuristics of instability and stabilization in model selection . Ann. Stat. 24 : 2350 – 2383 .
  • Buckland , S. T. , Burnham , K. P. , Augustin , N. H. ( 1997 ). Model selection: An integral part of inference . Biometrics 53 : 603 – 618 .
  • Bühlmann , P. , Yu , B. ( 2006 ). Sparse boosting . J. Machine Learn. Res. 7 : 1001 – 1024 .
  • Burnham , K. P. , Anderson , D. R. ( 2002 ). Model Selection and Multimodel Inference. , 2nd ed. New York : Springer .
  • Chatfield , C. ( 1995 ). Model uncertainty, data mining and statistical inference (with discussion) . J. R. Stat. Soc. Ser. B 158 : 419 – 466 .
  • Chen , C.-H. , George , S. L. ( 1985 ). The bootstrap and identification of prognostic factors via Cox's proportional hazards regression model . Stat. Med. 4 : 39 – 46 .
  • Copas , J. B. ( 1983 ). Regression, prediction and shrinkage (with discussion) . J. R. Stat. Soc. Ser. B 45 : 311 – 354 .
  • Copas , J. B. , Long , T. ( 1991 ). Estimating the residual variance in orthogonal regression with variable selection . Statistician 40 : 51 – 59 .
  • Efron , B. ( 1979 ). Bootstrap methods: Another look at the jackknife . Ann. Stat. 7 : 1 – 26 .
  • Efron , B. ( 1983 ). Estimating the error rate of a prediction rule: Improvement on cross-validation . J. Am. Stat. Assoc. 78 : 316 – 331 .
  • Efron , B. , Tibshirani , R. J. ( 1993 ). An Introduction to the Bootstrap . New York : Chapman & Hall/CRC .
  • Efron , B. , Tibshirani , R. J. ( 1997 ). Improvements on cross-validation: The .632 + bootstrap method . J. Am. Stat. Assoc. 92 : 548 – 560 .
  • Ein-Dor , L. , Zuk , O. , Domany , E. (2006). Thousands of samples are needed to generate a robust gene list for predicting outcome in cancer. Proc. Natl. Acad. Sci. USA 103:5923–5928.
  • Gerds , T. A. , Cai , T. , Schumacher , M. ( 2008 ). The performance of risk prediction models . Biometr. J. 50 : 457 – 479 .
  • Gifi , J. ( 1990 ). Nonlinear Multivariate Analysis . Chichester : John Wiley & Sons .
  • Gong , G. ( 1986 ). Cross-validation, the jackknife, and bootstrap: Excess error in forward logistic regression . J. Am. Stat. Assoc. 81 : 108 – 113 .
  • Gunter , L. , Zhu , J. , Murphy , S. ( 2011 ). Variable selection for qualitative interactions in personalized medicine while controlling the family-wise error rate . J. Biopharm. Stat. this issue .
  • Harrell , F. E. ( 2001 ). Regression Modeling Strategies, with Applications to Linear Models, Logistic Regression, and Survival Analysis . New York : Springer .
  • Meinshausen , N. , Bühlmann , P. ( 2010 ). Stability selection . J. R. Stat. Soc. Ser. B 72 : 417 – 473 .
  • Miller , A. J. ( 1984 ). Selection of subsets of regression variables (with discussion) . J. R. Stat. Soc. Ser. A 147 : 389 – 425 .
  • Miller , A. J. ( 2002 ). Subset Selection in Regression. , 2nd ed. Boca Raton , FL : Chapman & Hall/CRC .
  • Molinaro , A. M. , Simon , R. , Pfeiffer , R. M. ( 2005 ). Prediction error estimation: A comparison of resampling methods . Bioinformatics 21 : 3301 – 3307 .
  • Qiu , X. , Xiao , Y. , Gordon , A. , Yakovlev , A. ( 2006 ). Assessing stability of gene selection in microarray data analysis . BMC Bioinformatics 7 : 50 .
  • Rosenwald , A. , Wright , G. , Chan , W. C. , Connors , J. M. , Campo , E. , Fisher , R. I. , Gascoyna , R. D. , Muller-Hermelink , H. K. , Smeland , E. B. , Staudt , L. M. ( 2002 ). The use of molecular profiling to predict survival after chemotherapy for diffuse large-b-cell lymphoma . N. Engl. J. Med. 346 : 1937 – 1946 .
  • Royston , P. , Sauerbrei , W. ( 2003 ). Stability of multivariable fractional polynomial models with selection of variables and transformations: A bootstrap investigation . Stat. Med. 22 : 639 – 659 .
  • Royston , P. , Sauerbrei , W. ( 2008 ). Multivariable Model-Building: A Pragmatic Approach to Regression Analysis Based on Fractional Polynomials for Modelling Continuous Variables . Chichester , UK : Wiley .
  • Sauerbrei , W. ( 1999 ). The use of resampling methods to simplify regression models in medical statistics . J. R. Stat. Soc. Ser. C 48 : 313 – 329 .
  • Sauerbrei , W. , Royston , P. ( 1999 ). Building multivariable prognostic and diagnostic models: Transformation of the predictors using fractional polynomials . J. R. Stat. Soc. Ser. A 162 : 71 – 94 .
  • Sauerbrei , W. , Royston , P. ( 2007 ). Modelling to extract more information from clinical trials data—On some roles for the bootstrap . Stat. Med. 26 : 4989 – 5001 .
  • Sauerbrei , W. , Schumacher , M. ( 1992 ). A bootstrap resampling procedure for model building: Application to the Cox regression model . Stat. Med. 11 : 2093 – 2109 .
  • Sauerbrei , W. , Holländer , N. , Buchholz , A. ( 2008 ). Investigation about a screening step in model selection . Stat. Comput. 18 : 195 – 208 .
  • Sauerbrei , W. , Royston , P. , Schumacher , M. ( 2005 ). Bootstrap methods for developing predictive models [letter] . Am. Stat. 59 : 116 – 118 .
  • Schumacher , M. , Holländer , N. , Sauerbrei , W. ( 1997 ). Resampling and cross-validation techniques: A tool to reduce bias caused by model building? Stat. Med. 16 : 2813 – 2827 .
  • Simon , R. , Radmacher , M. , Dobbin , K. , McShane , L. M. ( 2003 ). Pitfalls in the use of DNA microarray data for diagnostic and prognostic classification . J. Natl. Cancer Inst. 95 : 14 – 18 .
  • Segal , M. ( 2006 ). Microarray gene expression data with linked survival phenotypes: Diffuse large-b-cell lymphoma revisited . Biostatistics 7 : 268 – 285 .
  • Steck , H. , Jaakkola , T. (2003). Bias-Corrected Bootstrap and Model Uncertainty. Advances in Neural Information Processing Systems 16 . In: Thrun , S. , Saul , L. K. , Schölkopf , B. , eds. Cambridge , MA : MIT Press.
  • Strobl , C. , Boulesteix , A.-L. , Zeileis , A. , Hothorn , T. ( 2007 ). Bias in random forest variable importance measures: Illustrations, sources and a solution . BMC Bioinformatics 8 : 25 .
  • Tibshirani , R. ( 1996 ). Regression shrinkage and selection via the lasso . J. R. Stat. Soc. Ser. B 58 : 267 – 288 .
  • van Houwelingen , H. , le Cessie , S. ( 1990 ). Predictive value of statistical models . Stat. Med. 9 : 1303 – 1325 .
  • Verweij , P. J. M. , van Houwelingen , H. ( 1993 ). Cross-validation in survival analysis . Stat. Med. 12 : 2305 – 2314 .
  • Zou , H. ( 2006 ). The adaptive lasso and its oracle properties . J. Am. Stat. Assoc. 101 : 1418 – 1429 .
  • Zou , H. , Hastie , T. ( 2005 ). Regularization and variable selection via the elastic net . J. R. Stat. Soc. B 67 : 301 – 320 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.